Weighted norm inequalities for general operators on monotone functions

Lai, Shanzhong

doi:10.1090/S0002-9947-1993-1132877-X

Weighted norm inequalities for general operators on monotone functions
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Trans. Amer. Math. Soc. 340 (1993), 811-836 Request permission

Abstract:

In this paper we characterize the weights $w,v$ for which ${\left \| {{S_\phi }f} \right \|_{p,w}} \leq C{\left \| f \right \|_{q,v}}$, for $f$ nonincreasing, where ${S_\phi }f = \smallint _0^\infty {\phi (x,y)f(y)dy}$.

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The weighted Hardy’s inequality for nonincreasing operators of monotone functions